A257595 - OEIS

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A257595

Expansion of x^3*(1+x+2*x^2+3*x^3+3*x^4+x^5)/(1-x^2-x^3)^3.

0, 0, 0, 1, 1, 5, 9, 18, 34, 58, 100, 164, 265, 421, 657, 1015, 1549, 2343, 3515, 5234, 7745, 11393, 16673, 24285, 35220, 50880, 73238, 105073, 150286, 214346, 304910, 432677, 612581, 865435, 1220209, 1717180, 2412276, 3383076, 4737076, 6623076, 9246855

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Jean-Luc Baril, and Jean-Marcel Pallo, A Motzkin filter in the Tamari lattice, Discrete Mathematics 338.8 (2015): 1370-1378.

Index entries for linear recurrences with constant coefficients, signature (0,3,3,-3,-6,-2,3,3,1 ).

FORMULA

G.f.: x^3*(1+x+2*x^2+3*x^3+3*x^4+x^5)/(1-x^2-x^3)^3.

MATHEMATICA

CoefficientList[Series[x^3(1+x+2x^2+3x^3+3x^4+x^5)/(1-x^2-x^3)^3, {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 3, 3, -3, -6, -2, 3, 3, 1}, {0, 0, 0, 1, 1, 5, 9, 18, 34}, 50] (* Harvey P. Dale, Feb 13 2022 *)

CROSSREFS

Sequence in context: A061502 A110349 A036832 * A116453 A046578 A046590

Adjacent sequences: A257592 A257593 A257594 * A257596 A257597 A257598

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 04 2015

STATUS

approved